It’s hard to imagine a world in which people with superhuman powers are just like you and me.

But that’s what co-creators Zak Penn and Michael Karnow are doing in the new Syfy series “Alphas.”

Five people working for a secret division of the Department of Defense solve crimes using their extraordinary “alpha” abilities — skills like hyper-persuasion, flawless aim and the ability to mentally process electromagnetic wavelengths without a computer.

That’s the gimmick.

When not actively using their abilities, the characters behave with relentless normality. They squabble over lunch, have romantic entanglements, drive a minivan and even run out of change for parking meters!

They were so normal, the network initially didn’t know what to make of the series.

“From the very beginning, the whole goal was to get as close to reality as we can possible make it without it being boring,” says Penn, best known for writing such blockbusters as “X-Men: The Last Stand” and “The Incredible Hulk.”

He recalls getting a note early on from Syfy asking about one character, “ ‘So basically, he’s no better than you or I? Why are we doing a show about him?’ “

The answer, of course, is that the writer thought it was necessary “to ground it in reality as much as we could, so that when those [superpower] moments happen, you really do believe in them,” Penn says.

“Alphas” began with Karnow’s “research about real CIA and Soviet KGB programs during the ’60s and ’70s, trying to recruit psychics and people with extraordinary abilities,” Penn says, adding that “most of [it] ended in hilarious failure.”

The idea also raised intriguing questions. What would happen if those programs actually worked or intelligence agencies had figured out how to use people with unusual abilities?

Combine that with Penn’s devotion to neurologist Oliver Sacks’ books and the notion of taking “the real-life equivalent of the stuff I sometimes write in movies and trying to make it as real as possible,” he says, and — zap! — “Alphas” was born.

All the special abilities possessed by the main characters, Penn says, have some real-world evidence they actually exist.

Three of the five superhuman abilities possessed by the main characters “are completely legitimate, we found references for all of that online,” he says. “We exaggerate how you see their powers, [but] they’re not things that are beyond the realm of reason,” he says.

For instance, one character — played by Malik Yoba — has super strength, which is a well-known attribute of the fight or flight response. Moving an inconveniently parked car or countering multiple attackers is not unheard-of.

“People have been documented doing things that are pretty close to the things he actually does. It’s just that they can’t usually do them at will,” Penn says.

Despite a background filled with movie explosions and big CGI pieces, “Alphas” is “not effects-driven,” he says. “I don’t want it to be that every single time Hicks [played by Warren Christie] does something, it’s amazing — like something you’ve never seen before.”

That’s why one of the first scenes he ever came up with shows Cameron Hicks — who possesses with flawless aim and dexterity — in the unglamorous act of throwing quarters into a vending machine from across the room.

“I’m kind of tired of the ever-expanding spectacle” of $150-million action movies that traffic in stunts merely because they have never been seen before, he says. “I like this idea of, ‘Oh my God, I could do that!’ ”

Although Penn is tight-lipped about spoilers, he does reveal that not all 12 episodes this season will involve chasing after an “evil alpha every week” and that a mysterious Red Flag group, introduced in the premiere, will play a much bigger role as the series progresses.

“We’re creating an organization and an opposition for our team that is not necessarily what you’d expect,” he hints. “This is not [‘Get Smart’s’] KAOS or the [‘X-Men’s’ evil] Brotherhood of Mutants.”

Penn also promises that “Alphas” will not devolve into campiness — a problem that has plagued past TV series involving superheroes or those with superhuman abilities. “That’s something that just doesn’t appeal to me,” he says, pausing before jokingly adding, “Except for the big musical episode, where there’s a Broadway play called ‘Alphas’ and they all become part of it.”